<chajadan@mail.com> wrote in message news:1180612896.731992.273150@x35g2000prf.googlegroups.com...>>> You do however have to give some sort of definition for 0.999...>> Whatever you define it to be it will either be equal to 1>> or it will not be a real number.>>>> My definition of 0.999... is the sum of all elements of an infinite> set defined by 0.9*(1/10)^n for all n in the set of wholes numbers> including 0 and is included in my proof. I do not attribute to this> entity any other characteristics, need not for it to be real or non-> real. I allow the consequence of the infinite contibutive values alone> to dictate all else.>

Infinite sum? Does it converge? Sounds like a limit to me.

>>> No. If you use the standard limit definition, 10x-x = 9.>> You are only correct if you use some other definition for>> 0.999... in which case the "subtraction" is not in the>> real numbers. You need to define a new set of "numbers".>> When you do so you will not get a field.>>>> - William Hughes>> I avoid all limit definitions. To me limits are their own area of> study that tell you potentially more about what bounds an entity that> about the entity itself.>> The limit of 1/x as x approaches infinity is 0, but this is not> representative of the function at all which will never yield a zero> value. I do not reject ideas that discuss and define 0.999... as a> limit - I only reject ideas that attempt use a limit to ~equate~ to> the entity described by that limit when this is not justified. I leave> this disclaimer only to take into account a constant limit, such as> the limit of 3 as x approaches infinity - where the limit is exactly> equal to the number that yields it.>

Mate, have a rethink, because this is contrary to what you just wrote.